Florida Republican Marco Rubio's strong third-place finish in the Iowa caucuses could accelerate his bid to secure Senate endorsements for his presidential campaign, supporters said Tuesday.

Rubio's campaign told Roll Call that in the aftermath of the showing in Iowa, aides have had conversations with many members of the House and Senate about endorsements.

In addition, the aide said that what was described as a handful of additional endorsements should be expected in the days ahead, with the message being that Rubio is best equipped to defeat Clinton in November.

One Senate Republican, South Carolina's Tim Scott, announced his support for Rubio on Tuesday, bringing the candidate's congressional endorsement total to five senators and 23 House members. Beyond the endorsements, several senators traveled to Iowa in the past few days to campaign for Rubio.

Cruz, the winner in Monday's caucuses, picked up an endorsement in the House from South Carolina Republican Jeff Duncan on Tuesday. He now has 19 endorsements in that chamber, but none from his fellow senators, according to Roll Call's Endorsement Tracker . Donald Trump, who came in second Monday, has no congressional backers.

"One is on a trend line that looks better than the other two, and that person is Rubio," Sen. James M. Inhofe, a conservative from Oklahoma, said of the top three finishers. "What I honestly believe is happening here, and the reason I feel so good about Rubio is that he's kind of been in a position where he can just be honest, respond, not be attacking, and you're seeing the other two attacking."

Still many lawmakers are expected to wait at least until next week's New Hampshire primary before committing.

"A lot of these candidates that are running sort of in that lane, the same lane, are going to try and make their case [in New Hampshire]," said Senate Republican Conference Chairman John Thune of South Dakota, who has yet to endorse anyone. "I think there's going to be a natural winnowing process."

Rubio received 23 percent of the Iowa caucus votes, coming in closer than expected to Trump, at 24 percent or Cruz at 28 percent. Scott said he decided to endorse Rubio after a series of town hall meetings with candidates in South Carolina, in advance of the state's primary this month.

"I am putting my confidence and my trust in Marco Rubio, because I believe that he takes us to that better future," Scott said in a video posted Tuesday morning. "Marco Rubio understands that here in America, it's not about where you start, it's about where you are going. We have one shot in 2016 to beat Hillary Clinton and that shot is Marco Rubio, and with him as our candidate: we win."

Scott is following up on his support by urging colleagues to join him.

"I've had some conversations. I hope that they're fruitful," he said. One of his targets could be Republican Sen. Mike Rounds of South Dakota, whose pick for the GOP nomination, former Arkansas Gov. Mike Huckabee, suspended his 2016 presidential bid Monday after failing to gain traction in Iowa.

Rounds was noncommittal Tuesday. "I want to visit with Mike [Huckabee] first, have a chance to visit with him and see what his thoughts are long-term and then go from there," he said.

In the House, Duncan joined the ranks of Cruz supporters Tuesday, saying in a statement, "I didn't run for Congress to make friends, I ran to fight to restore the America that we love. Sometimes in these fights I've been in the majority, other times I’ve been in the minority, and often I'm one of a few. But I've never been alone, and that is because Ted Cruz has been in the middle of nearly all of those fights with me."

Rubio supporter Sen. Jim Risch of Idaho said he thought the Senate's turn toward Rubio began before the results in Iowa became clear.

"I think there's movement in that regard, but it was happening even before last night," Risch told Roll Call. "It's starting."

Risch was among the lawmakers appearing at caucus sites in Iowa on behalf of candidates, as was Inhofe.

Republican Sens. Steve Daines of Montana and Cory Gardner of Colorado also made swings through Iowa for Rubio on Monday, a day when the Senate did not hold roll call votes.

One senator who does not intend to pick another horse is 2008 GOP nominee John McCain of Arizona, who has been on the campaign sidelines since his friend Sen. Lindsey Graham of South Carolina dropped out. Asked about the Iowa Republicans supporting Cruz, McCain pointed to his own poor electoral history in the Hawkeye State.

"I respect the verdict of the people, the caucus-goers in Iowa," McCain said. "I never had a close relationship with them."

Graham quickly backed former Florida Gov. Jeb Bush, for whom he has campaigned in New Hampshire.

Thune of South Dakota has not picked a candidate, having previously cited his leadership role within the party in the Senate and more than one of his members in the field. (Sen. Rand Paul, R-Ky., joins Cruz and Rubio in the presidential field.).

But he speculated that there may be more consolidation around a single candidate after the New Hampshire and South Carolina primaries, though he did note that he believed Rubio had a good night on Monday.

Along with a still-crowded field of candidates, Thune suggested lawmakers have also realized that their endorsements may not be helpful in the current climate, which has rewarded political outsiders.

"There are naturally, I think, endorsements that are coming from members of Congress," Thune said, "but I think most people are recognizing that endorsements from members of Congress have limited value in this environment."

A senior Rubio aide told Roll Call that Scott would travel to New Hampshire Friday to stump for Rubio, along with Rep. Trey Gowdy, a fellow South Carolinian. House Oversight and Government Reform Chairman Jason Chaffetz, R-Utah, is expected that this weekend's GOP debate in New Hampshire.